Kinovea is a video player for all sport enthusiasts.
Slow down,study and comment the technique of your athletes or of yourself.
It is 100% free and open source.Observe two videos side by side and synchronize them on a common event.

Welcome to SuperUser. Link-only answers are not very useful, so this needs some descriptive text.
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harrymcJun 9 '14 at 11:19

Doesn't seem to play audio, but if you don't need that (I didn't), it was super easy to install and get running in seconds and plays two videos side-by-side without any issues.
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hheimbuergerJun 15 '14 at 22:44

Voilà, you got synchronized playback. The kind where a single set of playback controls is used for all streams so you wouldn't have to "Invest in some finger weights and train yourself to click very quickly" as @ta.speot.is suggests.

vvvv is a hybrid graphical/textual programming environment for easy
prototyping and development. It is designed to facilitate the handling
of large media environments with physical interfaces, real-time motion
graphics, audio and video that can interact with many users
simultaneously.

Untested because my wine setup is completely screwed right now. It doesn't do side by side but stacked playback (unless you have a very good lcd you won't be seeing the same thing by playing the same vid in two opposite corners of the screen anyway)

If you think you really need side by side you can use avisynth to do what zimmer said.

Many players will be able to output a picture of a single frame in the video.

You could choose multiple points in your videos to compare different types of image (clouds, smoke, trees, grass, motion are good for encoding comparisons) and take the same frames from each of your videos.

You can then make comparisons on a static image rather than trying to spot differences in motion. You can compare on a pixel by pixel basis if you want.

Ensure you don't use JPG as the output though as this is a lossy format and will introduce its own artefacts.

I image you can use an AutoHotKey script to send a "Play" shortcut to all three players in a very short amount of time.

Whether they are able to start playing at exactly the same time is a different matter. Even if they are able to start straight away, I imagine there will be some fighting for the hard drive. Might want to make a RAM disk if this is an important evaluation.